The invention relates to the general field of current measuring instruments, and more particularly to current transformers for fitting on board an aircraft.
The use of current transformers (CT) is common practice in aviation on alternating current (AC) networks operating at 115 volts AC (VAC) or at 230 VAC. CTs are used to measure AC line currents in airplane networks, which are generally three-phase AC networks.
As shown in FIG. 1, a CT is constituted by a magnetic circuit, which is generally in the form of a torus in order to minimize magnetic leakage, and which has a number n of secondary turns wound thereon that are looped via a load resistance. Those turns carry a current written I2. The current, written I1, that is to be measured in the busbar passes through the resulting torus at least once. In the example described herein and as shown in particular in FIG. 2, which is a simplified electrical circuit diagram of a CT, it is assumed that the number of primary turns is equal to one (as is usual in aviation).
A CT complies with Ampere's law, which is written mathematically by the following equation:
      ∮                  H        →            ⁢                          ⁢                        d          ⁢                                          ⁢          I                →              =            -              I        1              +          nI      2      where I1 is the current to be measured passing through the torus, I2 corresponds to the measurement current obtained by winding n turns around the magnetic core, and H is the magnetic field used for magnetizing the torus.
Ignoring any circulation of the magnetic field in the core, i.e. assuming
            ∮                        H          →                ⁢                                  ⁢                              d            ⁢                                                  ⁢            I                    →                      =    0    ,then the following relationship is obtained: I1=nI2.
The secondary circuit is loaded by a load resistance, written RB in FIG. 2, which makes it possible, by measuring the voltage across the terminals of the load resistance, to deduce the voltage VB across the secondary of the torus, which is given by
            V      B        =                            R          B                ⁢                  I          2                    =                        R          B                ⁢                              I            1                    n                      ,ignoring magnetizing current, and thus to determine the current I1 flowing in the busbar passing through the torus.
CTs thus present the advantage of being capable of taking a measurement that is relatively insensitive to the electromagnetic environment within the airplane and transmitting it to the control and protection members, referred to respectively as the general control unit (GCU) and the bus power control unit (BPCU). CTs can thus easily be remote from the decision-taking members, being spaced apart from them by a few tens of centimeters to several tens of meters on board an airplane.
Nevertheless, using CTs raises a problem. When a CT is open circuit (no load resistance), i.e. when the connection between the CT and its receiver, a CGU or a BPCU or even some other member, is interrupted, then a high voltage is generated at the output from the secondary windings of the CT. Specifically, the lack of current flowing in the secondary leads to equality between the primary current and the circulation of the magnetizing field used for magnetizing the torus. This gives
      ∮                  H        →            ⁢                          ⁢                        d          ⁢                                          ⁢          I                →              =      -                  I        1            .      
Since the amplitude of the primary current that is to be measured is generally quite high, the induction B in the magnetic circuit becomes saturated very quickly each time the primary current reverses. By applying Lenz's law to the secondary of the CT, V=ndφ/dt, where φ is the electromagnetic flux exchanged between the primary and secondary, it is found that the voltage takes on values that are very large on each sudden change in the magnetizing current. This voltage depends on the number of secondary turns, on the type of the magnetic core, and also on the value of the primary current that is to be measured.
This high voltage, which depends on the value of the measured current, can easily exceed several kilovolts. It can lead to electric arcs being struck at the output from the CT, or even within its windings. The triggering of such phenomena thus depends on the level of current flowing in the lines that are to be measured, and also on the magnetic material used for the CT and on its number of secondary turns.
In an airplane this can lead to non-negligible risk, since these phenomena continue to be maintained so long as they have not been detected, and they can give rise to a fire.
There exist three main types of protection families for protecting CTs: protection by adding a bidirectional peak-limiter; protection by adding a resistance in parallel with the output of the CT; and protection by adding a capacitor.
As shown in FIG. 3, protection by means of a peak-limiter is obtained by connecting a peak-limiter, e.g. such as a tranzorb, between the two outputs of the CT. The peak-limiter is set to a voltage higher than the maximum voltage VCT_out to be measured across the terminals of the load resistance RB. When the CT is open circuit, the power dissipated by the peak-limiter may be written as follows:
      〈    P    〉    =                    V        T                    n        ⁢                                  ⁢        π              ⁢          I      primary_rms        ⁢          2        ⁢          (              1        -                  cos          ⁡                      (                          ωΔ              ⁢                                                          ⁢              t                        )                              )      
With
            Δ      ⁢                          ⁢      t        =                  nS        ⁢                              Δ            ⁢                                                  ⁢                          B              cc                                            V            T                              =              f        ⁡                  (                      V            T                    )                      ,and where VT represents the peak-limiting voltage, Δt the duration of peak-limiting, ω the angular frequency of the electrical power network, S the effective cross-sectional area of the magnetic material, ΔBcc the maximum peak-to-peak induction of the magnetic material, n the number of secondary turns, and Iprimary_rms the primary root mean square (rms) current for which it is desired to protect the CT.
As can be seen in FIG. 4, losses depend on the peak-limiting voltage, and also on the primary current, on the number of turns, on the cross-section of the core, and on the level of saturation of the magnetic material.
For an application on a three-phase network operating at 90 kilovolt amps (kVA) and 400 hertz (Hz), the peak limiting voltage should generally be selected to be greater than 40 volts (V). Thus, if the losses of the CT (ignoring the iron losses of the core) are estimated, then the following distribution is to be found: 0.36 watts (W) for copper losses in the secondary, and 6.25 W for the peak-limiter type protection. Given the very large losses for the peak-limiter type protection, a heatsink must be provided to evacuate the power dissipated by this protection, since the peak-limiter runs the risk of not withstanding the temperature.
As shown in FIG. 5, the circuit conventionally used for providing protection by adding a resistance in parallel with the output of the CT comprises: the CT; a load resistance RB for measurement purposes; and a resistance Rp connected in parallel with the load resistance RB at the output from the CT. The losses in the parallel resistance Rp as a function of its resistance value are given by the curve in FIG. 6. This curve was obtained from a digital simulation model.
As shown by the curve in FIG. 7, when the parallel resistance Rp is too high, losses are reduced, however the peak voltage is attenuated very little. In contrast, when the resistance is very low, i.e. of the order of no more than about 100 ohms, losses are low and the output voltage is limited, but under such circumstances, accuracy is not very high. Specifically, the measured current then depends on the line impedance, which has a value that cannot be known with great accuracy.
The current ICTout flowing in the measurement resistance may be expressed as a function of the input primary current:
      I    CTout    =                    i        1            n        ⁢                  R        p                    (                              R            p                    +                      R            B                    +                      R            l                          )            
It should be observed that the error concerning the measured current is of the same order of magnitude as the sum of the accuracies relating to the resistances Rp, Rl, and RB. Although RB and Rp can be accurate, Rl is subject to inaccuracy concerning knowledge about the length of the line.
As shown in FIG. 8, the circuit conventionally used for providing protection by adding a capacitor comprises: the CT; a load resistance RB; and a capacitor C connected in parallel with the output of the CT.
For this type of protection, it is necessary to choose an appropriate value for the capacitance of the capacitor. In order to determine the optimum value for the capacitance, it is considered that when the load resistance RB is disconnected, the output voltage must be less than the saturation voltage for a given rms current I1rms flowing in the primary turn (in general the nominal primary current).
An equivalent model is set up as shown in FIG. 9 in which the current IC flowing in the capacitor is equal to I1 (t)/n, with n being the number of secondary turns in the CT, and including a resistance Rω corresponding to the resistance of the secondary winding.
The current IC flowing through the capacitance is then given by:
      I    C    =      C    ⁢                  dV        CTout            dt      
Where C is the capacitance of the capacitor and VCTout is the voltage across the terminals of the CT, and thus across the terminals of the capacitor.
The voltage across the terminals of the windings is given by:
  V  =                    V        CTout            +                        R          ω                ⁢                  I          CTout                      =                            1          C                ⁢                  ∫                                    I                              CT                out                                      ⁢            dt                              +                        R          ω                ⁢                  I          CTout                    
With ICTout being the current delivered by the CT, i.e. in the equivalent model, the current flowing in the winding and the resistance Rω of the secondary winding.
The current flowing in the capacitance can also be expressed as a function of the primary current I1rms.
      I    CTout    =                    I                  1          ⁢                                          ⁢          rms                    n        ⁢          2        ⁢          sin      ⁡              (                  ω          ⁢                                          ⁢          t                )            
Thus, under sinusoidal conditions, this gives:
  V  =            (                                    -            j                    ⁢                      1                          C              ⁢                                                          ⁢              ω                                      +                  R          ω                    )        ⁢          I      CTout      
From which it can be deduced:
  V  =                              (                                    1                                                (                                      C                    ⁢                                                                                  ⁢                    ω                                    )                                2                                      +                          R              ω              2                                )                    ⁢                                I          CTout                              =                            (                                    1                                                (                                      C                    ⁢                                                                                  ⁢                    ω                                    )                                2                                      +                          R              ω              2                                )                    ⁢                        I                      1            ⁢                                                  ⁢            rms                          n            ⁢              2            
By writing Lentz's law as follows:
  V  =            n      ⁢                        d          ⁢                                          ⁢          φ                dt              =          nS      ⁢                        d          ⁢                                          ⁢          B                dt            likewise under sinusoidal conditions:∥V∥=nSω∥B∥
It can be deduced therefrom that:
      nS    ⁢                  ⁢    ω    ⁢                B              =                    (                              1                                          (                                  C                  ⁢                                                                          ⁢                  ω                                )                            2                                +                      R            ω            2                          )              ⁢                  I                  1          ⁢                                          ⁢          rms                    n        ⁢          2      
Which can be developed as follows:
                              n          2                ⁢        S        ⁢                                  ⁢        ω        ⁢                            B                                                I                      1            ⁢                                                  ⁢            rms                          ⁢                  2                      =                  (                              1                                          (                                  C                  ⁢                                                                          ⁢                  ω                                )                            2                                +                      R            ω            2                          )                                (                                            n              2                        ⁢            S            ⁢                                                  ⁢            ω            ⁢                                        B                                                                        I                              1                ⁢                                                                  ⁢                rms                                      ⁢                          2                                      )            2        =          (                        1                                    (                              C                ⁢                                                                  ⁢                ω                            )                        2                          +                  R          ω          2                    )                  1                        (                      C            ⁢                                                  ⁢            ω                    )                2              =                            (                                                    n                2                            ⁢              S              ⁢                                                          ⁢              ω              ⁢                                              B                                                                                    I                                  1                  ⁢                                                                          ⁢                  rms                                            ⁢                              2                                              )                2            -              R        ω        2            
  C  =            1      ω        ⁢                  1                                            (                                                                    n                    2                                    ⁢                  S                  ⁢                                                                          ⁢                  ω                  ⁢                                                          B                                                                                                            I                                          1                      ⁢                                                                                          ⁢                      rms                                                        ⁢                                      2                                                              )                        2                    -                      R            ω            2                              
The capacitance actually selected should be greater than the above-determined value in order to avoid saturation of the magnetic core.
  C  >            1      ω        ⁢                  1                                            (                                                                    n                    2                                    ⁢                  S                  ⁢                                                                          ⁢                  ω                  ⁢                                                                          ⁢                                      B                    max                                                                                        I                                          1                      ⁢                                                                                          ⁢                      rms                                                        ⁢                                      2                                                              )                        2                    -                      R            ω            2                              
The major drawback of this solution is that it is difficult to use for providing differential protection. Specifically, in the event of a short circuit, the capacitor currents can be identified by the differential protection as being a differential fault current.
Other kinds of protection also exist that generally make use of active electronics, thereby reducing the overall reliability of the current measuring device including the CT. That is why this type of protection is not used.
Adding protection, such as resistances, for example, to the CT generally leads to a loss of accuracy in the final output measurement. This loss of accuracy then gives rise to a need to raise the fault detection thresholds, in particular for differential faults.
Furthermore, such protection is generally not capable of withstanding a permanent fault. It can thus likewise lead to overheating and starting a fire.